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La stratification naturelle des espaces de fonctions différentiables réelles et le théorème de la pseudo-isotopie

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1007/bf02684889openalex-snapshot
Stability of C ∞ mappings, IV. Classification of stable germs by R -algebras
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Stability of C ∞ mappings, III. Finitely determined map-germs
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Sur les difféomorphismes de la sphère de dimension trois (Γ4 = O)
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Concordance and isotopy of 𝑃𝐿 embeddings
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Lectures on the H-Cobordism Theorem
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Stability of C ∞ Mappings: I. The Division Theorem
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Stability of C ∞ Mappings: II. Infinitesimal Stability Implies Stability
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Sur les représentations induites des groupes de Lie
inferredcites →https://doi.org/10.24033/bsmf.1567openalex-snapshot
Topologie de certains espaces de plongements

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Reeb graphs of curves are stable under function perturbations
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Real versus Complex Robustness Margin Continuity as a Smooth versus Holomorphic Singularity Problem
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Thick tangles
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The Work of Stephen Smale in Differential Topology
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The Smale—Hirsch Principle in Catastrophe Theory
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Signatures of Monic Polynomials
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Old and New Results on Density of Stable Mappings
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Some Ideas in Need of Clarification in Resolution of Singularities and the Geometry of Discriminants
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Pachner’s Theorem
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Multiparameter Persistent Homology via Generalized Morse Theory
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Stein Structures: Existence and Flexibility
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Stable Shape Comparison of Surfaces via Reeb Graphs
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Spacetime Weave—Bit as the Connection Between Its or the Informational Content of Spacetime
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Floer Field Philosophy
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On the Geometry and Topology of the Commutator of Unit Quaternions
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K-Theory and Geometric Topology
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Differential Topology Interacts with Isoparametric Foliations
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Embedded 2-Spheres in ℝ3
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Sausages and Butcher Paper
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Surgery on the Novikov complex
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The stability theorem for smooth pseudoisotopies
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A non-Abelian K-theory and pseudo-isotopies of 3-manifolds
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The Borel regulator map on pictures, II: An example from Morse theory
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Deformation of Morse functions. I
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Topology of spaces of functions without compound singularities
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Global gravitational anomalies
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Ends of maps, II
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Concordance and isotopy of smooth embeddings in low codimensions
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Conjugaison topologique des germes de fonctions holomorphes � singularit� isol�e en dimension trois
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A calculus for framed links inS 3
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Isotopie de formes ferm�es en dimension trois
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Symplectic topology as the geometry of generating functions
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Sur les fibrations de Milnor de familles d'hypersurfaces � lieu singulier de dimension un
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The L�-Ramanujam problem for hypersurfaces with one-dimensional singular sets
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A parametrized index theorem for the algebraic K-theory Euler class
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Formes differentielles fermées non singulières sur len-tore
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Engouffrement symplectique et intersections lagrangiennes
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A curious remark concerning the geometric transfer map
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Formes différentielles de degré 1 fermées non singulières: Classes d'homotopie de leurs noyaux
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On some problems in singularity theory
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The shift equivalence problem
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Isotopy classes of periodic diffeomorphisms on spheres
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Hochschild homology and the second obstruction for pseudoisotopy
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Homotopy groups of automorphism spaces
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The pseudo-isotopy theorem for simply connected differentiable manifolds
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The bifurcation subset of a space of maps
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Algebraic invariants for pseudo-isotopies
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Homotopie des espaces de concordances [d’après F. Waldhausen]
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A survey of diffeomorphism groups
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Pseudo-isotopy and K2
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Involutions and isotopies of lens spaces
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Quelques problemes globaux sur les fonctions de Morse
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Geometric properties of generic differentiable manifolds
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Stability of minimal surfaces
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H-cobordisms, pseudo-isotopies, and analytic torsion
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Minimal morse functions
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Seidel–Smith cohomology for tangles
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Mapping class groups of highly connected $$(4k+2)$$-manifolds
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K -theoretic invariants for Floer homology
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Concordance and Isotopy of Metrics with Positive Scalar Curvature
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The equivariant pair-of-pants product in fixed point Floer cohomology
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Finiteness and infiniteness results for Torelli groups of (hyper-)Kähler manifolds
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The extra-nice dimensions
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On Kontsevich’s characteristic classes for higher dimensional sphere bundles I: the simplest class
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Elimination of extremal index zeroes from generic paths of closed $$1$$ 1 -forms
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Harmonic cellular maps which are not diffeomorphisms
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A homological approach to pseudoisotopy theory. I
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Bourgeois contact structures: Tightness, fillability and applications
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The Edit Distance for Reeb Graphs of Surfaces
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Diffeomorphisms and Almost Complex Structures on Tori
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Common stabilizations of amalgamated Heegaard splitting and dual Heegaard splitting
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Some Algebraic Properties of Cerf Diagrams of One-Parameter Function Families
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A Morse complex on manifolds with boundary
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On a class of immersions of spheres into space forms of nonpositive curvature
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Remarks on the oscillation energy of Legendrian isotopies
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Differential topology of adiabatically controlled quantum processes
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Diffeomorphism Stability and Codimension Three
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G-Topological quantum field theory
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Nearly Frobenius algebras
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Moduli spaces of morse functions for persistence
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Fiber of persistent homology on morse functions
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Harmonic Spinors
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The geometry of tensor calculus, I
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A note on the codimension of a map
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Fibered knots and algebraic singularities
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Pseudo-isotopies et isotopies en dimension quatre dans la categorie topologique
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On special generic maps from a closed manifold into the plane
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Topology of special generic maps of manifolds into Euclidean spaces
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ON πi DIFF Mn
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Isoparametric foliations, diffeomorphism groups and exotic smooth structures
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A geometric Morse–Novikov complex with infinite series coefficients
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Stability of Reeb Graphs of Closed Curves
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Gluing diffeomorphisms, bi-Lipschitz mappings and homeomorphisms
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Birth and death in discrete Morse theory
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Standard special generic maps of homotopy spheres into Euclidean spaces
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Handle homology of manifolds
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The connectedness homomorphism between discrete Morse complexes
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Bar-Natan theory and tunneling between incompressible surfaces in 3-manifolds
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Connecting discrete Morse functions via birth-death transitions
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Differential topology of numerical range
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Isotopy invariants for smooth tori in 4-manifolds
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Smooth models for certain fibered partially hyperbolic systems
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The homology of moduli spaces of 4-manifolds may be infinitely generated
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Pseudo-isotopies of simply connected 4-manifolds
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The cohomology of Torelli groups is algebraic
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Kirby diagrams of 4-dimensional open books
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Deformations of real analytic functions and the natural stratification of the space of real analytic functions
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Low-dimensional concordances, Whitney towers and isotopies
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Homology stability for symmetric diffeomorphism and mapping class groups
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Direct sum decompositions and indecomposable TQFTs
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CRITICAL POINTS OF SMOOTH FUNCTIONS AND THEIR NORMAL FORMS
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Complexes of curves and the Teichmüller modular group
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Linkings and Pfaff's equations
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On the topology of spaces of functions without complex singularities
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Embedding of compacta, stable homotopy groups of spheres, and singularity theory
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Combinatorics of fronts of Legendrian links and the Arnol'd 4-conjectures
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$ K_2$ for the simplest integral group rings and topological applications
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The framed Morse complex and its invariants
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A survey of the homology cobordism group
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Lectures on Field Theory and Topology
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Lectures on Differential Topology
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The 4-dimensional light bulb theorem
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Numerical control over complex analytic singularities
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The Powell Conjecture for the genus-three Heegaard splitting of the 3-sphere
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The second obstruction for pseudo-isotopies
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Bordism groups of special generic mappings
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The Homotopy Type of the Space of Diffeomorphisms. I
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Piecewise Linear Bundles in the Metastable Range
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Differentiable group actions on homotopy spheres. III. Invariant subspheres and smooth suspensions
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The Space of Framed Functions
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A Note on Local Change of Diffeomorphism
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Construction by Isotopy. II
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Pseudo-Isotopies of Irreducible 3-Manifolds
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Approximation of Approximate Fibrations by Bundle Maps
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The Alexander and Markov Theorems Via Diagrams for Links in 3-Manifolds
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Metrics of positive scalar curvature and generalised Morse functions, Part II
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Simplifying stable mappings into the plane from a global viewpoint
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Metrics of positive scalar curvature and generalised Morse functions, part I
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Diffeomorphisms of manifolds with finite fundamental group
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The Cobordism hypothesis
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Strong shift equivalence theory and the shift equivalence problem
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Exact Lagrangian immersions with a single double point
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Morse index of a cyclic polygon. II
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The Convenient Setting of Global Analysis
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Self-covering, finiteness, and fibering over a circle
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Enhanced Bruhat Decomposition and Morse Theory
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On the Geometry of Some Equivariantly Related Manifolds
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Smooth Compactness for Spaces of Asymptotically Conical Self-Expanders of Mean Curvature Flow
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The Disc Embedding Theorem
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Copyright Page
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Preface
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List of figures
inferred← citeshttps://doi.org/10.1093/oso/9780198841319.003.0001openalex-snapshot
Context for the Disc Embedding Theorem
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Outline of the Upcoming Proof
inferred← citeshttps://doi.org/10.1093/oso/9780198841319.003.0003openalex-snapshot
The Schoenflies Theorem after Mazur, Morse, and Brown
inferred← citeshttps://doi.org/10.1093/oso/9780198841319.003.0004openalex-snapshot
Decomposition Space Theory and the Bing Shrinking Criterion
inferred← citeshttps://doi.org/10.1093/oso/9780198841319.003.0005openalex-snapshot
The Alexander Gored Ball and the Bing Decomposition
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A Decomposition That Does Not Shrink
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The Whitehead Decomposition
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Mixed Bing–Whitehead Decompositions
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Shrinking Starlike Sets
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The Ball to Ball Theorem
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Intersection Numbers and the Statement of the Disc Embedding Theorem
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Gropes, Towers, and Skyscrapers
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Picture Camp
inferred← citeshttps://doi.org/10.1093/oso/9780198841319.003.0014openalex-snapshot
Architecture of Infinite Towers and Skyscrapers
inferred← citeshttps://doi.org/10.1093/oso/9780198841319.003.0015openalex-snapshot
Basic Geometric Constructions
inferred← citeshttps://doi.org/10.1093/oso/9780198841319.003.0016openalex-snapshot
From Immersed Discs to Capped Gropes
inferred← citeshttps://doi.org/10.1093/oso/9780198841319.003.0017openalex-snapshot
Grope Height Raising and 1-storey Capped Towers
inferred← citeshttps://doi.org/10.1093/oso/9780198841319.003.0018openalex-snapshot
Tower Height Raising and Embedding
inferred← citeshttps://doi.org/10.1093/oso/9780198841319.003.0019openalex-snapshot
Good Groups
inferred← citeshttps://doi.org/10.1093/oso/9780198841319.003.0020openalex-snapshot
The s-cobordism Theorem, the Sphere Embedding Theorem, and the Poincaré Conjecture
inferred← citeshttps://doi.org/10.1093/oso/9780198841319.003.0021openalex-snapshot
The Development of Topological 4-manifold Theory
inferred← citeshttps://doi.org/10.1093/oso/9780198841319.003.0022openalex-snapshot
Surgery Theory and the Classification of Closed, Simply Connected 4-manifolds
inferred← citeshttps://doi.org/10.1093/oso/9780198841319.003.0023openalex-snapshot
Open Problems
inferred← citeshttps://doi.org/10.1093/oso/9780198841319.003.0024openalex-snapshot
Replicable Rooms and Boundary Shrinkable Skyscrapers
inferred← citeshttps://doi.org/10.1093/oso/9780198841319.003.0025openalex-snapshot
The Collar Adding Lemma
inferred← citeshttps://doi.org/10.1093/oso/9780198841319.003.0026openalex-snapshot
Key Facts about Skyscrapers and Decomposition Space Theory
inferred← citeshttps://doi.org/10.1093/oso/9780198841319.003.0027openalex-snapshot
Skyscrapers Are Standard: An Overview
inferred← citeshttps://doi.org/10.1093/oso/9780198841319.003.0028openalex-snapshot
Skyscrapers Are Standard: The Details
inferred← citeshttps://doi.org/10.1093/oso/9780198841319.003.0029openalex-snapshot
Afterword: PC4 at Age 40
inferred← citeshttps://doi.org/10.1093/qmath/haae035openalex-snapshot
Homotopy Theoretic Properties Of Open Books
inferred← citeshttps://doi.org/10.1109/cdc.1993.325854openalex-snapshot
Robust stability, Morse theory and singularity
inferred← citeshttps://doi.org/10.1109/cdc.1997.652348openalex-snapshot
Real versus complex robustness margin continuity as a smooth versus holomorphic singularity problem
inferred← citeshttps://doi.org/10.1109/cdc42340.2020.9303908openalex-snapshot
Nonconvex optimization on data manifold by accelerated curvature transport
inferred← citeshttps://doi.org/10.1109/vis60296.2025.00024openalex-snapshot
Analyzing Time-Varying Scalar Fields using Piecewise-Linear Morse-Cerf Theory
inferred← citeshttps://doi.org/10.1112/jtopol/jtr007openalex-snapshot
The decategorification of sutured Floer homology
inferred← citeshttps://doi.org/10.1112/jtopol/jtv007openalex-snapshot
Exotic spheres and the topology of symplectomorphism groups
inferred← citeshttps://doi.org/10.1112/plms/pdw042openalex-snapshot
Elimination of cusps in dimension 4 and its applications
inferred← citeshttps://doi.org/10.1112/topo.12063openalex-snapshot
On the classification of 1-connected 7-manifolds with torsion free second homology
inferred← citeshttps://doi.org/10.1112/topo.12085openalex-snapshot
Link cobordisms and functoriality in link Floer homology
inferred← citeshttps://doi.org/10.1112/topo.12168openalex-snapshot
Tangle Floer homology and cobordisms between tangles
inferred← citeshttps://doi.org/10.1112/topo.12283openalex-snapshot
Families of diffeomorphisms and concordances detected by trivalent graphs
inferred← citeshttps://doi.org/10.1112/topo.12324openalex-snapshot
Some rational homology computations for diffeomorphisms of odd‐dimensional manifolds
inferred← citeshttps://doi.org/10.1112/topo.70043openalex-snapshot
Pseudo‐isotopies and diffeomorphisms of 4‐manifolds
inferred← citeshttps://doi.org/10.1134/s1061920814010087openalex-snapshot
Group structures on some families of 6-manifolds
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